Dzhaliuk Nataliia Semenivna

Education: Drohobych Ivan Franko State Pedagogical University (specialty – mathematics and computer sciences, 2001),

Postgraduate of Pidstryhach Institute for APMM NAS of Ukraine (01.01.06 – algebra and number theory, 2009)   

Scientific degree: Ph.D. Degree (01.01.06 – algebra and number theory, 2010) ( thesis: "Factorization of matrices over polynomial and similar to them rings")

Scientific title: Docent

Position: Senior Research Fellow (since 2018)

In Institute: from 2001

Research interests: linear algebra, matrix theory, matrix equations, matrices over commutative rings.

Major publications:

1.Matrix linear bilateral equations over different domains, methods for construction of solutions and description of their structure. Math. methods and phys.-mech.  fields. 65,No. 1-2,  18-41, (2022). (in Ukrainian)

2.The structure of the Smith normal form of the greatest common divisor and the least common multiple of the third order matrices over Bezout domains of stable range 1.5 (with Romaniv A. M.).  Applied problems of mechanics and mathematics. Vol 20, 25–30, (2022). (in Ukrainian)

3.Solutions of the matrix equation AX + YB = C with triangular coefficients. Journal of Mathematical Sciences. 261, No. 1, 25–32, (2022) https://doi.org/10.1007/s10958-022-05734-x. (Scopus, 0.534, Q3)

4.Equivalence of matrices in the ring M(n,R) and its subrings (with Petrychkovych V.M.). Ukrainian Mathematical Journal. 73, No.12, 1865– 1872, (2022). https://doi.org/10.1007/s11253-022-02034-0. (Scopus, 0.726, Q3)

5.Existence of the solution of the Sylvester-type matrix equation in the ring of block triangular matrices. Applied problems of mechanics and mathematics. 19, 79−83, (2021). (in Ukrainian)

6.Equivalence of matrices in the ring M(n,R) and in its subrings (with Petrychkovych V.M.). Ukrainian Mathematical Journal. 73, (12), 1612–1618, (2021). DOI: 10.37863/umzh.v73i12.6858 (in Ukrainian)

7.Solutions of matrix equation AX+YB=C with triangular coefficients. Mat. Metody Fiz.-Mekh. Polya. 62, (2), 26–31, (2019). (in Ukrainian)

8.Some relationships between the invariant factors of matrix and its submatrix over elementary divisor domains. (with Romaniv A. M.). Applied problems of mechanics and mathematics. 17, 38−41, (2019).

9.Solutions of  the matrix linear bilateral polynomial  equation and their structure. (with Petrychkovych V.M.). Algebra and Discrete Mathematics. 27, (2), 243–251, (2019). (Scopus, 0.782, Q3)

10.  Factorizations in the matrix ring and its subrings of the block matrices (with Petrychkovych V.M.). The Fourth Conference of Mathematical Society of the Republic of Moldova: dedicated to the centenary of Vladimir Andrunachievici (1917-1997): Proceedings CMSM 4, June 28 – July 2, 2017 Chisinau / ed.: Mitrofan Choban [et al.]. Chisinau: Institute of Mathematics and Computer science, (CEP USM), 143–146, (2017).

11.  Factorizations in the rings of the block matrices (with Petrychkovych V.M.). Bul. Acad. Stiinte Repub. Mold. Mat. 85 (3), 23–33, (2017). (Scopus, 0.649, Q4).

12.  The structure of solutions of the matrix linear unilateral polynomial equation with two variables (with Petrychkovych V.M.). Carpathian Math. Publ. 9, (1), 48–56, (2017). (Web of Science, Q4)

13.  Absolute factorization of matrices in the rings of block-triangular matrices (with Petrychkovych V.M.). Applied problems of mechanics and mathematics. 11, 36 – 40, (2013). (in Ukrainian)

14.  The matrix linear unilateral and bilateral equations with two variables over commutative rings. (with Petrychkovych V.M.). ISRN Algebra, Volume 2012, Article ID 205478, 14 pages, doi: 10.5402/2012/205478.

15.  Semiscalar equivalence of polynomial matrices and the solutions of the Sylvester matrix polynomial equations. (with Petrychkovych V.M.). Mathematical bulletin of the Shevchenko scientific society. 9, 81–88, (2012). (in Ukrainian)

16.  Solutions of matrix polynomial Diophantine equation (with Petrychkovych V.M.). Applied problems of mechanics and mathematics. 10, 55 – 61, (2012). (in Ukrainian)

17.  The block diagonal parallel factorizations of matrices over principal ideal domains. Journal of National University "Lvivska Politechnika" “Physical & mathematical sciences”. 740, 5 – 10, (2012). (in Ukrainian)

18.  The matrix Diophantine equations AX+ BY= C (with Petrychkovych V.M.). Carpathian Mathematical Publications. 3 (2), 49–56, (2011). (in Ukrainian)

19.  The association of factorizations of block triangular matrices and of their diagonal blocks over commutative principal ideal domains. Applied problems of mechanics and mathematics. 9, 82 – 86, (2011). (in Ukrainian)

20.  Parallel factorizations of matrices over rings and their connections (with Petrychkovych V.M.). Applied problems of mechanics and mathematics. 8, 7 – 17, (2010). (in Ukrainian)

21.  The uniqueness of the cell-triangular factorizations of the matrices over a principal ideal rings. Reports of the Academy of Sciences of Ukraine. 1, 7 – 12, (2010).  (in Ukrainian)

22.  Description of parallel factorizations of polynomial matrices. Scientific bulletin of Uzhorod university. Series Mathematics and Informatics. 19, 31 – 37, (2009). (in Ukrainian)

23.  Common divisors of the block-triangular matrices over principal ideal domains. Applied problems of mechanics and mathematics. 7, 86 – 90, (2009). (in Ukrainian)

24.  Factorization of block diagonal and block triangular matrices over principal ideal rings (with Petrychkovych V.M.). Mathematical bulletin of the Shevchenko scientific society. 4, 79–89, (2007). (in Ukrainian)

25.  On solution of matrix polynomial equations and on similarity of matrices (with Petrychkovych V.M.). Mat. Metody Fiz.-Mekh. Polya.   48, ( 4), 14 – 19, (2005). (in Ukrainian)

26.  On common monic divisors of polynomial matrices with given canonical diagonal form (with Petrychkovych V.M.). Mat. Metody Fiz.-Mekh. Polya .  45,  ( 3),  7 – 13, (2002). (in Ukrainian)

List of Conference Proceedings:

  1. Dzhaliuk Nataliia, Petrychkovych Vasyl'. Solvability of matrix equation AX=YB in the ring of block triangular matrices // Current problems of Mechanics and Mathematics – 2023: Collection of Scientific Papers / Edited by Roman M. Kushnir (Academician of NAS of Ukraine) and Volodymyr O. Pelykh (Corresponding Member of NAS of Ukraine) [Published Online] // Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine. – 2023. – 454 p. – Access by the link: http://iapmm.lviv.ua/mpmm2023/materials/proceedings.mpmm2023.pdf P. 405-406. - http://iapmm.lviv.ua/mpmm2023/materials/ma10_13.pdf
  2. Dzhaliuk Nataliia, Petrychkovych Vasyl'. The Sylvester matrix polynomial equation and its solutions // 14th Ukraine Algebra Conference, July 3-7, 2023 Sumy, Ukraine. Book of Abstracts: Sumy State Pedagogical University named after A.S. Makarenko, Sumy, Ukraine. - 150 p. - P. 54
  3. Dzhaliuk Nataliia. Linear solutions to the bilateral matrix polynomial equations // Materials of the international scientific conference dedicated to the 55th anniversary of the Faculty of Mathematics and Informatics, September 28-30, 2023 - Chernivtsi: Chernivtsi National University, 2023. – 369 p. – P. 47–48.
  4. Dzhaliuk N. S. Ðîçâ'ÿçêè ñòåïåíÿ s ìàòðè÷íîãî ïîëiíîìiàëüíîãî ðiâíÿííÿ Cèëüâåñòðà // XIX International Scientific Mykhailo Kravchuk Conference, dedicated to the 125th anniversary of Igor Sikorsky Kyiv Polytechnic Institute. Proceedings of Nineteenth International Scientific Mykhailo Kravchuk Conference, October 11–12, 2023, Kyiv, Igor Sikorsky Kyiv Polytechnic Institute.- P. 104-105. - https://matan.kpi.ua/en/kravchuk-conf-2023/
  5. Petrychkovych V.M., Dzhaliuk N.S. Application of special triangular forms of matrices with respect to equivalences of different types to solving linear matrix equations of Sylvester type // International Algebraic Conference "At the End of the Year" 2021, December 27–28, 2021, Kyiv, Ukraine, Abstracts: Kyiv. – 36 p. – P. 20.
  6. Dzhaliuk N., Petrychkovych V. Solutions of matrix linear Sylvester type equations // International Conference in Complex and Functional Analysis dedicated to the memory of Bohdan Vynnytskyi. September 13–16, 2021, Drohobych, Ukraine. Book of Abstracts: Drohobych State Pedagogical University of Ivan Franko, Drohobych, Ukraine. – 67 p. – P. 15.

7.     Nataliia Dzhaliuk, Vasyl' Petrychkovych Block matrices, their equivalences and applications // The 13th International Algebraic Conference in Ukraine. July 6–9, 2021, Taras Shevchenko National University of Kyiv. Book of Abstracts: Taras Shevchenko National University of Kyiv, Kyiv, Ukraine. – 94 p. – [Electronic resource]. – Access mode: https://bit.ly/3hcTbKe – P. 34.

  1. Nataliia Dzhaliuk Equivalence of matrices in the ring of the block triangular matrices // XI International Skorobohatko Mathematical Conference. October 26−30, 2020, Lviv, Ukraine. Abstracts: Lviv: Pidstryhach Institute for Applied Problems of Mechanics and Mathematics, 2020. – 130 p. – [Electronic resource]. – Access mode: http://www.iapmm.lviv.ua/conf_skorob2020/documents/2020tezy.pdf – P. 29.
  2. Petrychkovych V.M., Dzhaliuk N.S. Solvability of the matrix Sylvester-type equation in the ring of the block triangular matrices // Book of abstracts of the International mathematical conference dedicated to the 60th anniversary of the department of algebra and mathematical logic of Taras Shevchenko National University of Kyiv, 14-17 July 2020, Kyiv, Ukraine. – 93 p. – [Electronic resource]. – Access mode: https://bit.ly/2ZIyqMs – P. 63.
  3. Romaniv A.M., Dzhaliuk N.S. Some connections between invariant factors of matrix and its submatrix // International Scientific Conference Algebraic and Geometric Methods of Analysis, 26-30 may 2020, Odesa, Ukraine. – 131 p. – Access mode: https://www.imath.kiev.ua/~topology/conf/agma2020/agma-2020-abstracts/agma2020-theses.pdf – P. 57.
  4. Nataliia Dzhaliuk. Solutions of the Sylvester matrix equation with triangular coefficients // The XII International Algebraic Conference in Ukraine dedicated to the 215th anniversary of V.Bunyakovsky. July 02-06, 2019, Vinnytsia, Ukraine. Abstracts/ Vinnytsia: Vasyl' Stus Donetsk National University, 2019. – 142 p. – P. 28–29. http://jiac.donnu.edu.ua/article/view/6933/6964
  5. Dzhaliuk N., Petrychkovych V. Triangular solutions of matrix equation AX+YB=C // Modern problems of Mechanics and Mathematics: collection of scientific papers in 3 vol. / Edited by A.Ì. Samoilenko, R.M. Kushnir [Electronic resource] // Pidstryhach Institute for Applied Problems of Mechanics and Mathematics NAS of Ukraine. – 2018. – Vol. 3. – Access mode: www.iapmm.lviv.ua/mpmm2018. P. 197–198. (in Ukrainian)
  6. Petrychkovych V.M., Dzhaliuk N.S. A bound on degrees of solutions of the matrix linear bilateral polynomial equation // Book of abstracts of the XI International Algebraic Conference in Ukraine dedicated to the 75th anniversary of V.V.Kirichenko (July, 2017, Kyiv, Ukraine). P.99.
  7. Petrychkovych V.M., Dzhaliuk N.S. Structure of solutions of the matrix Diofantine polynomial equations //  International Algebraic Conference dedicated to 100th anniversary of L.A. Kaluzhnin. Book of Abstracts. Jule 7–12, 2014. Kyiv. – P. 29.
  8. Dzhaliuk N., Petrychkovych V. Factorizations in rings of block diagonal matrices // International Conference “Modern Problems of Mechanics and Mathematics”. – L’viv, Ukraine May 21–25, 2013., L’viv. Abstract. – L’viv: YA. S. Pidstryhach Institute for APMM NAS of Ukraine. – V. 3. – P. 181-183. (in Ukrainian)
  9. Dzhaliuk N., Petrychkovych V. Semiscalar equivalence of polynomial matrices and solutions of the matrix linear polynomial equations // 9-th International algebraic conference in Ukraine, L'viv, July 8-13, 2013: Book of abstracts. – L'viv, 2013. – P. 57.
  10. Dzhaliuk N., Petrychkovych V. Factorizations of block triangular matrices and their number // International Conference dedicated to the 120th anniversary of Stefan Banach, Lviv, Ukraine, 17–21 September 2012. Abstracts of Reports. – P. 268.
  11. Vasyl` Petrychkovych, Nataliia Dzhaliuk The matrix Diophantine polynomial equations // International Conference on Algebra dedicated to 100th anniversary of S.M. Chernikov, August 20-26, 2012, Dragomanov National Pedagogical University, Kiev, Ukraine: Book of abstracts. – Kiev: Institute of Mathematics of UNAS, 2012. – P. 116.
  12. Dzhaliuk N., Petrychkovych V. On the minimal degree solutions of the Sylvester matrix polynomial equations // International mathematical conference: abstracts of talks. – Mykolayiv: Published by Mykolayiv V.O. Suchomlinsky National University, 2012. – P. 138.
  13. Dzhaliuk N. S. The block diagonal parallel factorizations of matrices over principal ideal domains // Conference materials of young Scientists “ Pidstryhach reading – 2012”. – L’viv, Ukraine, May 23–25, 2012. – P 32–35. L’viv. – [Electronic resource]. – Access mode: http://www.iapmm.lviv.ua/chyt2012/materials/12.pdf (in Ukrainian)
  14. Dzhaliuk N.S., Petrychkovych V.M. The uniqueness of block diagonal parallel factorizations of matrices // 10-th Open scientific conference IMFS: [«PSC-IMFS-10»], (L’viv, Ukraine, May 17–18, 2012.) / Lviv Polytechnic National University. — L’viv: Lviv Polytechnic Publishing House, 2012. — P. A32 – [Electronic resource]. – Access mode: http://psc-imfs.conference.lviv.ua/messages/psc-imfs-10-proceedings_175x250.pdf (in Ukrainian)
  15. Dzhaliuk N.S., Petrychkovych V.M. Block triangular matrices with absolute divisors separation // XIV International Scientific Kravchuk mathematical conference. – Kyiv, Ukraine , April 19-21, 2012: Ê.: Conference materials. – P. 87. (in Ukrainian)
  16. Dzhalyuk N. S. The association of factorizations of block-triangular matrices // IV Conference of young Scientists Pidstryhach with Modern Problems of Mechanics and Mathematics. – L’viv, Ukraine, May 24–27, 2011. Abstract. – L’viv: YA. S. Pidstryhach Institute for APMM NAS of Ukraine. – P. 241-242. (in Ukrainian)

24.  Petrychkovych V. M., Dzhaliuk N. S. Factorizations in rings of block triangular matrices // 8th International Algebraic Conference in Ukraine . – Lugansk, Ukraine, July 5 – 12, 2011, Book of abstracts . – Lugansk Taras Shevchenko National University, Ukraine – P. 159.

  1. Petrychkovych V.M., Dzhaliuk N.S. Matrix Diophantine equations // International Skorobohatko mathematical conference. – Drohobych, Ukraine, September 19–23, 2011. Abstracts – P. 161. (in Ukrainian)
  2. Petrychkovych V.M., Dzhaliuk N.S. The uniqueness of solutions of matrix linear unilateral polynomial equations with two variables // All-Ukrainian Scientific Conference "Application of Mathematical Methods in Science and Technology", November 25-26, 2011. Abstracts. – Lutsk, 2011. – P. 70–72. (in Ukrainian)
  3. Dzhalyuk N. S. Equivalence and factorizations of partitioned matrices // 7th Inter­natio­nal Algebraic Conference in Ukraine, 18 – 23 August, 2009: Abstract of talks. – Kharkov, 2009. – Ð. 49.
  4. Dzhalyuk N. S. The divisors of polynomial matrices with parallel condition // Conference of young Scientists Pidstryhach with Modern Problems of Mechanics and Mathematics. – L’viv, Ukraine, May 25–27, 2009, –P. 168 – 170. (in Ukrainian)
  5. Dzhalyuk N. S. On the factorizations of block triangular matrices and their uniqueness // XII international Scientific Kravchuk mathematical conference. – Kyiv, Ukraine , May 15-17, 2008: Conference materials. – Ê.: TOV „Zadruha" – 600 p. – P. 600. (in Ukrainian)
  6. Nataliia Dzhalyuk, Vasyl’ Petrychkovych On common divisors of cell-triangular matrices // International Conference “Modern Problems of Mechanics and Mathematics” devoted to the 80th anniversary of the birth of academician Pidstryhach Ya. S. and the 30th anniversary IAPMM he founded. – L’viv, Ukraine May 25–29, 2008, L’viv. Abstract. – L’viv: YA. S. Pidstryhach Institute for APMM NAS of Ukraine. – V. 3. – P. 184 – 185. (in Ukrainian)
  7. Nataliia Dzhalyuk, Vasyl’ Petrychkovych The factorizations of block triangular integer matrices // International Skorobohatko mathematical conference. – Drohobych, Ukraine, September 24–28, 2007. Abstracts – P.  88. (in Ukrainian)
  8. Nataliya Dzhalyuk, Vasyl’ Petrychkovych Factorizations of partitioned matrices and solutions of linear matrix equations // 6th Inter­natio­nal Algebraic Conference in Ukraine, 1 – 7 July, 2007: Abstracts of talks. – Kamyanets-Podilsky, 2007. – P. 75 – 76.

Phone service: (032) 258 96 22

E-mail: nataliya.dzhalyuk@gmail.com